Propagating radial waves of travel cost in a grid

To calculate the minimum cost of travel to each location within a geographical area from a specified set of locations, most geographic information systems represent that area as a rectangular grid of discrete cells, each indicating the cost of traversing that cell's particular location. These increments of cost are then accumulated by proceeding from cell to adjacent cell in a manner that resembles the propagation of waves. Because this propagation is limited to the eight directions associated with each cell's eight neighbors, however, it is often misdirected, and travel costs are therefore often overestimated. This article discusses the context, precedent, design, implementation, performance, and implications of a new algorithm that eliminates such problems in a straightforward manner. It does so by retaining the octangular propagation mechanism of earlier algorithms while keeping track of the particular locations at which propagated waves of accumulating travel cost either refract or diffract. The approach also holds promise for significant improvement in areas ranging from dispersion modeling and shape analysis to interpolation and the delineation of cost-minimizing paths.